import os 
os.getcwd()
print(os.getcwd())
## 获取当前工作目录

import pandas as pd
from pandas import DataFrame   #数据框的简写，本书采用的是该格式，直接使用DataFrame即可
import numpy as np 
import matplotlib
import matplotlib.pyplot as plt
import seaborn as sns
plt.rcParams['font.sans-serif']=['SimHei']
plt.rcParams['axes.unicode_minus'] = False

#pd.set_option('display.max_rows', None) #显示所有数据行 
pd.set_option('display.max_rows',10)     #共显示10行数据
pd.set_option('display.max_columns',None)# 设置查看列不省略
pd.set_option('display.precision',2)#设置后四位
pd.options.display.float_format='{:.2f}'.format # 全局设置二位小数

#爬取标普500数据，12-2至12-10分钟级收盘价数据，创建demo数据库
import datetime as dt
import yfinance as yf

def get_data_tocsv(url=r'.\sp500tickers.xlsx'):
    msft = yf.Ticker('SPY')
    hist = msft.history(start="2024-12-2", end="2024-12-10", interval="1m")
    lie_all=hist['Close'].rename('SPY',inplace=True)
    df = pd.read_excel(url)
    for i in df.iloc[:,0]:
        msft=yf.Ticker(i)
        hist=msft.history(start="2024-12-2", end="2024-12-10", interval="1m")
        lie=hist['Close'].rename(i,inplace=True)
        lie_all=pd.concat([lie_all,lie],axis=1)
    lie_all.to_csv('sp500_data.csv')
    return lie_all
    
get_data_tocsv()

from sklearn.preprocessing import StandardScaler
data_origin=pd.read_csv(r'.\sp500_data.csv')
data_origin.rename(columns={data_origin.columns[0]: 'time'}, inplace=True)
data_origin.set_index(data_origin.columns[0], inplace=True)#设置时间为索引
data_origin.info()
#需要剔除的列 AZO,BKNG,NVR,POOL,BF.B,TPL,AIZ,BRK.B,CINF,ERIE,FDS,EG,MTD,BR,HUBB,JBHT,NDSN,SNA,GWW,FICO,TYL
need_to_drop=['AZO','BKNG','NVR','POOL','BF.B','TPL','AIZ','BRK.B','CINF','ERIE','FDS','EG','MTD','BR','HUBB','JBHT','NDSN','SNA','GWW','FICO','TYL']
data=data_origin.drop(need_to_drop,axis=1).bfill()#删除列和填充缺失值
missing_values = data.isnull().sum().sum()#查看是否还有缺失值
print(missing_values)
scaler = StandardScaler()#标准化
data = pd.DataFrame(scaler.fit_transform(data), columns=data.columns)
data.head()#查看数据
y_data = data['SPY'] #分开自变量和因变量
x_data = data.drop('SPY', axis=1)
x_data.shape

<class 'pandas.core.frame.DataFrame'>
Index: 2340 entries, 2024-12-02 09:30:00-05:00 to 2024-12-09 15:59:00-05:00
Columns: 504 entries, SPY to XEL
dtypes: float64(504)
memory usage: 9.0+ MB
0

(2340, 482)

from scipy.stats import pearsonr, spearmanr, kendalltau
from xicor.xicor import Xi
plt.rcParams['font.sans-serif']=['SimHei']
plt.rcParams['axes.unicode_minus'] = False
from scipy.stats import pearsonr, spearmanr, kendalltau
from xicor.xicor import Xi

from numpy import array, random, arange

def xicor(X, Y, ties=True):
    # 设置随机种子（可选）
    # random.seed(42)
    
    # 获取数据长度
    n = len(X)
    
    # 根据X的值对索引进行排序
    order = array([i[0] for i in sorted(enumerate(X), key=lambda x: x[1])])
    
    if ties:
        # 计算每个元素在Y中的排名
        l = array([sum(y >= Y[order]) for y in Y[order]])
        
        # 初始化r为l的副本
        r = l.copy()
        
        # 处理并列的情况
        for j in range(n):
            tie_count = sum(r[j] == r[i] for i in range(n))
            if tie_count > 1:
                tie_index = array([r[j] == r[i] for i in range(n)])
                r[tie_index] = random.choice(r[tie_index] - arange(0, tie_count), tie_count, replace=False)
        
        # 计算XICOR相关系数
        return 1 - n * sum(abs(r[1:] - r[:n-1])) / (2 * sum(l * (n - l)))
    else:
        # 计算每个元素在Y中的排名
        r = array([sum(y >= Y[order]) for y in Y[order]])
        
        # 计算XICOR相关系数（不处理并列情况）
        return 1 - 3 * sum(abs(r[1:] - r[:n-1])) / (n**2 - 1)

# 示例用法
X = [1, 2, 3, 4, 5]
Y = [5, 4, 3, 2, 1]
print(xicor(X, Y, ties=True))

def comparison_xicor_difference_pdf(calculation ,title_name='各种分布假定下的xicor系数对sin函数的衡量',gap=5,n=50):
    beta=[];binomial=[];chisquare=[];exponential=[];f=[];gamma=[]
    geometric=[];gumbel=[];laplace=[];logistic =[];lognormal =[];
    negative_binomial=[];noncentral_chisquare=[];noncentral_f=[];
    norm=[];pareto=[];t=[];uniform=[];weibull=[];
    for i in [gap*a for a in range(n)]:
        x_beta=np.random.beta(a=2,b=2,size=i+2)
        x_binomial=np.random.binomial(n=10,p=0.5,size=i+2)
        x_chisquare=np.random.chisquare(df=5,size=i+2)
        x_exponential=np.random.exponential(scale=1,size=i+2)
        x_f=np.random.f(dfnum=2, dfden=2,size=i+2)
        x_gamma=np.random.gamma(shape=5,scale=1,size=i+2)
        x_geometric=np.random.geometric(p=0.5,size=i+2)
        x_gumbel=np.random.gumbel(loc=0,scale=1,size=i+2)
        x_laplace=np.random.laplace(loc=0,scale=1,size=i+2)
        x_logistic=np.random.logistic(loc=0,scale=1,size=i+2)
        x_lognormal=np.random.lognormal(mean=0,sigma=1,size=i+2)
        x_negative_binomial=np.random.negative_binomial(n=5,p=0.5,size=i+2)
        x_noncentral_chisquare=np.random.noncentral_chisquare(df=5,nonc=5,size=i+2)
        x_noncentral_f=np.random.noncentral_f(dfnum=5,dfden=5,nonc=5,size=i+2)
        x_norm=np.random.normal(loc=0,scale=1,size=i+2)
        x_pareto=np.random.pareto(a=5,size=i+2)
        x_t=np.random.standard_t(df=5,size=i+2)
        x_uniform=np.random.uniform(low=0,high=1,size=i+2)
        x_weibull=np.random.weibull(a=5,size=i+2)
        y_beta=calculation(x_beta)
        y_binomial=calculation(x_binomial)
        y_chisquare=calculation(x_chisquare)
        y_exponential=calculation(x_exponential)
        y_f=calculation(x_f)
        y_gamma=calculation(x_gamma)
        y_geometric=calculation(x_geometric)
        y_gumbel=calculation(x_gumbel)
        y_laplace=calculation(x_laplace)
        y_logistic=calculation(x_logistic)
        y_lognormal=calculation(x_lognormal)
        y_negative_binomial=calculation(x_negative_binomial)
        y_noncentral_chisquare=calculation(x_noncentral_chisquare)
        y_noncentral_f=calculation(x_noncentral_f)
        y_norm=calculation(x_norm)
        y_pareto=calculation(x_pareto)
        y_t=calculation(x_t)
        y_uniform=calculation(x_uniform)
        y_weibull=calculation(x_weibull)
        beta.append(max(Xi(list(x_beta),list(y_beta)).correlation,Xi(list(y_beta),list(x_beta)).correlation))
        binomial.append(max(Xi(list(x_binomial),list(y_binomial)).correlation,Xi(list(y_binomial),list(x_binomial)).correlation))
        chisquare.append(max(Xi(list(x_chisquare),list(y_chisquare)).correlation,Xi(list(y_chisquare),list(x_chisquare)).correlation))
        exponential.append(max(Xi(list(x_exponential),list(y_exponential)).correlation,Xi(list(y_exponential),list(x_exponential)).correlation))
        f.append(max(Xi(list(x_f),list(y_f)).correlation,Xi(list(y_f),list(x_f)).correlation))
        gamma.append(max(Xi(list(x_gamma),list(y_gamma)).correlation,Xi(list(y_gamma),list(x_gamma)).correlation))
        geometric.append(max(Xi(list(x_geometric),list(y_geometric)).correlation,Xi(list(y_geometric),list(x_geometric)).correlation))
        gumbel.append(max(Xi(list(x_gumbel),list(y_gumbel)).correlation,Xi(list(y_gumbel),list(x_gumbel)).correlation))
        laplace.append(max(Xi(list(x_laplace),list(y_laplace)).correlation,Xi(list(y_laplace),list(x_laplace)).correlation))
        logistic.append(max(Xi(list(x_logistic),list(y_logistic)).correlation,Xi(list(y_logistic),list(x_logistic)).correlation))
        lognormal.append(max(Xi(list(x_lognormal),list(y_lognormal)).correlation,Xi(list(y_lognormal),list(x_lognormal)).correlation))
        negative_binomial.append(max(Xi(list(x_negative_binomial),list(y_negative_binomial)).correlation,Xi(list(y_negative_binomial),list(x_negative_binomial)).correlation))
        noncentral_chisquare.append(max(Xi(list(x_noncentral_chisquare),list(y_noncentral_chisquare)).correlation,Xi(list(y_noncentral_chisquare),list(x_noncentral_chisquare)).correlation))
        noncentral_f.append(max(Xi(list(x_noncentral_f),list(y_noncentral_f)).correlation,Xi(list(y_noncentral_f),list(x_noncentral_f)).correlation))
        norm.append(max(Xi(list(x_norm),list(y_norm)).correlation,Xi(list(y_norm),list(x_norm)).correlation))
        pareto.append(max(Xi(list(x_pareto),list(y_pareto)).correlation,Xi(list(y_pareto),list(x_pareto)).correlation))
        t.append(max(Xi(list(x_t),list(y_t)).correlation,Xi(list(y_t),list(x_t)).correlation))
        uniform.append(max(Xi(list(x_uniform),list(y_uniform)).correlation,Xi(list(y_uniform),list(x_uniform)).correlation))
        weibull.append(max(Xi(list(x_weibull),list(y_weibull)).correlation,Xi(list(y_weibull),list(x_weibull)).correlation))

        
        
    
    plt.figure()
    plt.plot(range(n), beta, marker=None, label='beta')
    plt.plot(range(n), binomial, marker=None, label='binomial')
    plt.plot(range(n), chisquare, marker=None, label='chisquare')
    plt.plot(range(n), exponential, marker=None, label='exponential')
    plt.plot(range(n), f, marker=None, label='f')
    plt.plot(range(n), gamma, marker=None, label='gamma')
    plt.plot(range(n), geometric, marker=None, label='geometric')
    plt.plot(range(n), gumbel, marker=None, label='gumbel')
    plt.plot(range(n), laplace, marker=None, label='laplace')
    plt.plot(range(n), logistic, marker=None, label='logistic')
    plt.plot(range(n), lognormal, marker=None, label='lognormal')
    plt.plot(range(n), negative_binomial, marker=None, label='negative_binomial')
    plt.plot(range(n), noncentral_chisquare, marker=None, label='noncentral_chisquare')
    plt.plot(range(n), noncentral_f, marker=None, label='noncentral_f')
    plt.plot(range(n), norm, marker=None, label='norm')
    plt.plot(range(n), pareto, marker=None, label='pareto')
    plt.plot(range(n), t, marker=None, label='t')
    plt.plot(range(n), uniform, marker=None, label='uniform')
    plt.plot(range(n), weibull, marker=None, label='weibull')
    plt.title(title_name);plt.xlabel('样本数/{}'.format(gap));plt.ylabel('rho_Value');plt.grid(False)
    # 显示图例,网格（可选）
    plt.legend(loc='upper left', bbox_to_anchor=(1, 1))
    plt.show()

comparison_xicor_difference_pdf(lambda x: np.sin(x),n=50)

c:\anaconda\envs\pytorch\lib\site-packages\xicor\xicor.py:81: RuntimeWarning: invalid value encountered in scalar divide
  return 1 - self.mean_absolute / self.inverse_g_mean

# #R语言的RDC 函数
# rdc <- function(x,y,k,s) {
#   x  <- cbind(apply(as.matrix(x),2,function(u) ecdf(u)(u)),1)
#   y  <- cbind(apply(as.matrix(y),2,function(u) ecdf(u)(u)),1)
#   wx <- matrix(rnorm(ncol(x)*k,0,s),ncol(x),k)
#   wy <- matrix(rnorm(ncol(y)*k,0,s),ncol(y),k)
#   cancor(cbind(cos(x%*%wx),sin(x%*%wx)), cbind(cos(y%*%wy),sin(y%*%wy)))$cor[1]
# }
# x <- matrix(c(1, 2, 3, 4), nrow = 2, byrow = TRUE)
# y <- matrix(c(5, 6, 7, 8), nrow = 2, byrow = TRUE)
# result <- rdc(x, y, k = 5, s = 1)
# cat(sprintf("%.7f\n", result))
#随机相依系数函数实现
from scipy.stats import rankdata
from scipy.linalg import svd

def rdc(x, y, k, s):
    # Convert to numpy arrays if they are not already
    x = np.array(x)
    y = np.array(y)
    
    # Apply ECDF to each column of x and y
    x_ecdf = np.apply_along_axis(lambda u: rankdata(u, method='max') / len(u), axis=0, arr=x)
    y_ecdf = np.apply_along_axis(lambda u: rankdata(u, method='max') / len(u), axis=0, arr=y)
    
    # Add a column of ones
    x = np.c_[x_ecdf, np.ones(x.shape[0])]
    y = np.c_[y_ecdf, np.ones(y.shape[0])]
    
    # Generate random matrices wx and wy
    wx = np.random.normal(0, s, (x.shape[1], k))
    wy = np.random.normal(0, s, (y.shape[1], k))
    
    # Compute the projections
    x_proj = np.cos(np.dot(x, wx)) + 1j * np.sin(np.dot(x, wx))
    y_proj = np.cos(np.dot(y, wy)) + 1j * np.sin(np.dot(y, wy))
    
    # Compute the canonical correlation
    Ux, Sx, Vx = svd(x_proj, full_matrices=False)
    Uy, Sy, Vy = svd(y_proj, full_matrices=False)
    
    # Compute the correlation matrix
    cor_matrix = np.dot(Ux.T, Uy)
    
    # Return the first canonical correlation coefficient
    return np.abs(cor_matrix).max()

# Example usage:
x = [[1, 2], [3, 4]]
y = [[5, 6], [7, 8]]
print(rdc(x, y, k=5, s=0))

1.0

#衡量交互效应
def interaction_effect_three(pdf_type='difference',choose='x1',gap=5,min_=0,max_=100,n=50):
    x1_112=[];x1_113=[];x1_122=[];x1_133=[];x1_123=[];
    x2_112=[];x2_122=[];x2_123=[];x2_223=[];x2_233=[];
    x3_113=[];x3_123=[];x3_133=[];x3_223=[];x3_233=[];
    for i in [gap*a for a in range(n)]:
        if pdf_type=='difference':
            x1=np.linspace(min_,max_,i+2) #生成i+2个数据点
            x2=np.random.randint(min_,max_,i+2)
            x3=np.random.binomial(int(max_),0.5,i+2)
        elif pdf_type=='Bernoulli':
            x1=np.random.binomial(1,0.5,i+2) #生成i+2个数据点
            x2=np.random.binomial(1,0.5,i+2)
            x3=np.random.binomial(1,0.5,i+2)
        elif pdf_type=='binomial':
            x1=np.random.binomial(int(max_),0.5,i+2)
            x2=np.random.binomial(int(max_),0.5,i+2)
            x3=np.random.binomial(int(max_),0.5,i+2)
            
        x1x1x2=x1*x1*x2;x1x1x3=x1*x1*x3;x1x2x2=x1*x2*x2;x1x3x3=x1*x3*x3;
        x1x2x3=x1*x2*x3;x2x2x3=x2*x2*x3;x2x3x3=x2*x3*x3
        
        if choose=='x1':
            x1_112.append(max(Xi(list(x1),list(x1x1x2)).correlation,Xi(list(x1x1x2),list(x1)).correlation))
            x1_113.append(max(Xi(list(x1),list(x1x1x3)).correlation,Xi(list(x1x1x3),list(x1)).correlation))
            x1_122.append(max(Xi(list(x1),list(x1x2x2)).correlation,Xi(list(x1x2x2),list(x1)).correlation))
            x1_133.append(max(Xi(list(x1),list(x1x3x3)).correlation,Xi(list(x1x3x3),list(x1)).correlation))
            x1_123.append(max(Xi(list(x1),list(x1x2x3)).correlation,Xi(list(x1x2x3),list(x1)).correlation))
            
        if choose=='x2':
            x2_112.append(max(Xi(list(x2),list(x1x1x2)).correlation,Xi(list(x1x1x2),list(x2)).correlation))
            x2_122.append(max(Xi(list(x2),list(x1x2x2)).correlation,Xi(list(x1x2x2),list(x2)).correlation))
            x2_123.append(max(Xi(list(x2),list(x1x2x3)).correlation,Xi(list(x1x2x3),list(x2)).correlation))
            x2_223.append(max(Xi(list(x2),list(x2x2x3)).correlation,Xi(list(x2x2x3),list(x2)).correlation))
            x2_233.append(max(Xi(list(x2),list(x2x3x3)).correlation,Xi(list(x2x3x3),list(x2)).correlation))
         
        if choose=='x3':
            x3_113.append(max(Xi(list(x3),list(x1x1x3)).correlation,Xi(list(x1x1x3),list(x3)).correlation))
            x3_123.append(max(Xi(list(x3),list(x1x2x3)).correlation,Xi(list(x1x2x3),list(x3)).correlation))
            x3_133.append(max(Xi(list(x3),list(x1x3x3)).correlation,Xi(list(x1x3x3),list(x3)).correlation))
            x3_223.append(max(Xi(list(x3),list(x2x2x3)).correlation,Xi(list(x2x2x3),list(x3)).correlation))
            x3_233.append(max(Xi(list(x3),list(x2x3x3)).correlation,Xi(list(x2x3x3),list(x3)).correlation))
           
    if choose=='x1':
        y1=x1_112;y2=x1_113;y3=x1_122;y4=x1_133;y5=x1_123
        label1=r'$\xi \left( x_1,x_1x_1x_2 \right) $'
        label2=r'$\xi \left( x_1,x_1x_1x_3 \right) $'
        label3=r'$\xi \left( x_1,x_1x_2x_2 \right) $'
        label4=r'$\xi \left( x_1,x_1x_3x_3 \right) $'
        label5=r'$\xi \left( x_1,x_1x_2x_3 \right) $'
        
    if choose=='x2':
        y1=x2_112;y2=x2_122;y3=x2_123;y4=x2_223;y5=x2_233
        label1=r'$\xi \left( x_2,x_1x_1x_2 \right) $'
        label2=r'$\xi \left( x_2,x_1x_2x_2 \right) $'
        label3=r'$\xi \left( x_2,x_1x_2x_3 \right) $'
        label4=r'$\xi \left( x_2,x_2x_2x_3 \right) $'
        label5=r'$\xi \left( x_2,x_2x_3x_3 \right) $'
        
    if choose=='x3':
        y1=x3_113;y2=x3_123;y3=x3_133;y4=x3_223;y5=x3_233
        label1=r'$\xi \left( x_3,x_1x_1x_3 \right) $'
        label2=r'$\xi \left( x_3,x_1x_2x_3 \right) $'
        label3=r'$\xi \left( x_3,x_1x_3x_3 \right) $'
        label4=r'$\xi \left( x_3,x_2x_2x_3 \right) $'
        label5=r'$\xi \left( x_3,x_2x_3x_3 \right) $'
        
    plt.figure()
    plt.plot(range(n), y1, marker=None, label=label1)
    plt.plot(range(n), y2, marker=None, label=label2)
    plt.plot(range(n), y3, marker=None, label=label3)
    plt.plot(range(n), y4, marker=None, label=label4)
    plt.plot(range(n), y5, marker=None, label=label5)
    plt.title('{}的交互作用图'.format(choose));plt.xlabel('样本数/{}'.format(gap));plt.ylabel('rho_Value');plt.grid(False)
    plt.legend(loc='upper left', bbox_to_anchor=(1, 1))
    plt.show()

interaction_effect_three(pdf_type='difference',choose='x1',gap=5,min_=0,max_=100,n=500)

interaction_effect_three(pdf_type='difference',choose='x2',gap=5,min_=0,max_=100,n=500)

interaction_effect_three(pdf_type='difference',choose='x3',gap=5,min_=0,max_=100,n=500)

interaction_effect_three(pdf_type='Bernoulli',choose='x1',gap=5,min_=0,max_=100,n=500)

c:\anaconda\envs\pytorch\lib\site-packages\xicor\xicor.py:81: RuntimeWarning: invalid value encountered in scalar divide
  return 1 - self.mean_absolute / self.inverse_g_mean

interaction_effect_three(pdf_type='Bernoulli',choose='x2',gap=5,min_=0,max_=100,n=500)

interaction_effect_three(pdf_type='Bernoulli',choose='x3',gap=5,min_=0,max_=100,n=500)

interaction_effect_three(pdf_type='binomial',choose='x1',gap=5,min_=0,max_=100,n=500)

interaction_effect_three(pdf_type='binomial',choose='x2',gap=5,min_=0,max_=100,n=500)

interaction_effect_three(pdf_type='binomial',choose='x3',gap=5,min_=0,max_=100,n=500)

#模拟实验3
def comparison_single_varible(calculation,title_name=None,gap=5,min_=0,max_=100,n=50):
    pearson1=[];spearman1=[];kendall1=[];Xi1=[];rdc1=[];
    for i in [gap*a for a in range(n)]:
        # x1=np.random.normal(0,1,i+2)
        x1=np.linspace(min_,max_,i+2) #生成i+2个数据点
        y1=calculation(x1)
        pearson,pearson_p=pearsonr(x1, y1)
        spearman,spearman_p=spearmanr(x1, y1)
        kendall,kendall_p=kendalltau(x1, y1)
        # rdcr=rdc(x1, y1,5,1)
        Xir=max(Xi(list(x1),list(y1)).correlation,Xi(list(y1),list(x1)).correlation)
        # Xir_p=Xi(list(x1),list(y1)).pval_asymptotic(ties=True)
        pearson1.append(pearson)
        spearman1.append(spearman)
        kendall1.append(kendall)
        # rdc1.append(rdcr)
        Xi1.append(Xir)
        
        
    plt.figure()
    plt.plot(range(n), pearson1, marker=None, label='pearson')# 绘制pearson的折线图,marker='o'or's'
    plt.plot(range(n), spearman1, marker=None, label='spearman')# 绘制spearman数据集的折线图
    plt.plot(range(n), kendall1, marker=None, label='kendall')# 绘制kendall数据集的折线图
    plt.plot(range(n), Xi1, marker=None, label='Xi') # 绘制xicor数据集的折线图
    # plt.plot(range(n), rdc1, marker=None, label='rdc') # 绘制rdc数据集的折线图
    plt.title(title_name);plt.xlabel('样本数/{}'.format(gap));plt.ylabel('rho_Value');plt.legend();plt.grid(False)
    # 显示图例,网格（可选）
    plt.show()
    
    
comparison_single_varible(lambda x:np.cumsum(x),title_name=r'$y\propto \sum{x}$')   #模拟一个自变量为x的函数，y=x1+x2+x3+...+xn

comparison_single_varible(lambda x:pow(x,2)+pow(x,3),title_name=r'$y\propto x^2+x^3$') # y=x^2+x^3

comparison_single_varible(lambda x:np.exp(x),title_name=r'$y\propto exp(x)$') #y=exp(x)

comparison_single_varible(lambda x:np.sin(x),title_name=r'$y\propto sinx$',n=50) #y=sinx 样本量=250

# comparison_single_varible(lambda x:np.sin(x),title_name=r'$y\propto sinx$',n=500) #y=sinx 样本量=2500

comparison_single_varible(lambda x:np.sin(x)/x,title_name=r'$y\propto \frac{\sin x}{x}$',min_=0.1,n=50) #y=sinx/x 样本量=250

# comparison_single_varible(lambda x:x/np.sin(x),title_name=r'$y\propto \frac{x}{\sin x}$',min_=0.1,max_=100,n=50) #y=x/sinx 样本量=250

comparison_single_varible(lambda x:x/np.sin(x),title_name=r'$y\propto \frac{x}{\sin x}$',min_=0.1,max_=100,n=500) #y=x/sinx 样本量=2500

comparison_single_varible(lambda x:x/np.sin(x),title_name=r'$y\propto \frac{x}{\sin x}$',min_=0.1,max_=10000,n=50) #y=x/sinx 样本量=2500

comparison_single_varible(lambda x:x/np.sin(x),title_name=r'$y\propto \frac{x}{\sin x}$',min_=0.1,max_=200,n=500) #y=x/sinx 样本量=2500

comparison_single_varible(lambda x:pow(x,x),title_name=r'$y\propto x^x$',min_=0.1,n=50) #y=x^x 样本量=250

comparison_single_varible(lambda x:(pow(x,2.5)+x*np.sin(x**2)+np.log(x+1)+np.exp(x)/x)/10,min_=0.0001,max_=7,title_name=r'$y\propto x^{2.5}+xsin(x^2)+\ln \left( x+1 \right) -\frac{exp(x)}{x}$',n=50) #y=复杂函数 样本量=250

comparison_single_varible(lambda x:np.random.randint(x),title_name='无关系时',min_=0.1,n=50) #无关样本，样本量=250

comparison_single_varible(lambda x:np.random.randint(x),title_name='无关系时',min_=0.1,n=500) #无关样本，样本量=2500

#离散随机变量的分段函数情况
def dicrete_cut(x):
    y=[]
    for i in range(len(x)):
        if x[i]<5: y.append(-1)
        elif x[i]<10: y.append(0)
        else: y.append(1)
    return y
#连续随机变量的分段函数情况
def continue_cut(x):
    y=[]
    for i in range(len(x)):
        if x[i]<5:y.append(-1)
        elif x[i]<10: y.append(np.exp(-x[i])+10)
        elif x[i]<15: y.append(np.sin(x[i]))
        else: y.append(3)
    return y

comparison_single_varible(lambda x : dicrete_cut(x),title_name=r'$y\propto -1\left( x<5 \right) \cup 0\left( 5\leqslant x<10 \right) \cup 1\left( 10\leqslant x \right) $',min_=0.1,max_=20,n=50) #离散分段函数，样本量=2500

comparison_single_varible(lambda x : continue_cut(x),title_name='连续的分段函数',min_=0.1,max_=20,n=50) #'连续的分段函数'，样本量=250

comparison_single_varible(lambda x :np.sin(pow(x,2)+np.sin(x)),title_name='',min_=0,max_=10,n=50) #'连续的分段函数'，样本量=250

from sklearn.decomposition import PCA
from sklearn.preprocessing import StandardScaler


# 1.导入数据
X_scaled = x_data.to_numpy()

# 2. PCA降维
pca = PCA(n_components=6)
X_pca = pca.fit_transform(X_scaled)

# 主成分方向
components = pca.components_

# 3. 绘图
fig, ax = plt.subplots(1, 2, figsize=(12, 6), dpi=120)


# 投影后数据散点图
ax[0].scatter(X_pca[:, 0], X_pca[:, 1], c='magenta', alpha=0.7, edgecolors='k')
ax[0].set_title("主成分后的数据")
ax[0].set_xlabel("Principal Component 1")
ax[0].set_ylabel("Principal Component 2")

# 主成分方向的可视化
for i, (comp, var) in enumerate(zip(components, pca.explained_variance_)):
    ax[1].arrow(0, 0, comp[0] * var, comp[1] * var, 
                color=f'C{i}', width=0.02, head_width=0.1)#, label=f'PC{i+1}'
ax[1].scatter(X_scaled[:, 0], X_scaled[:, 1], c='lightgreen', alpha=0.7, edgecolors='k')
ax[1].legend()
ax[1].set_title("在原本空间上的主成分")
ax[1].set_xlabel("Feature 1")
ax[1].set_ylabel("Feature 2")

plt.tight_layout()
plt.show()

<matplotlib.collections.PathCollection at 0x1958fe7c790>

Text(0.5, 1.0, '主成分后的数据')

Text(0.5, 0, 'Principal Component 1')

Text(0, 0.5, 'Principal Component 2')

<matplotlib.patches.FancyArrow at 0x1959008ec10>

<matplotlib.patches.FancyArrow at 0x1959008eeb0>

<matplotlib.patches.FancyArrow at 0x19590045df0>

<matplotlib.patches.FancyArrow at 0x195900832b0>

<matplotlib.patches.FancyArrow at 0x19590083520>

<matplotlib.patches.FancyArrow at 0x195900834f0>

from sklearn.decomposition import FactorAnalysis
import seaborn as sns

#1. 数据准备
data = x_data
columns = x_data.columns

# 2. 因子分析
fa = FactorAnalysis(n_components=6, random_state=42)
fa.fit(data)

# 提取因子载荷矩阵和因子得分
factor_loadings = fa.components_.T
factor_scores = fa.transform(data)

# 3. 可视化
plt.figure(figsize=(12, 6))

# 因子载荷热力图
plt.subplot(1, 2, 1)
sort_df = pd.DataFrame(factor_loadings.T,columns=columns ).T
sort_df=sort_df.sort_values(by=[0,1], ascending=[False,False]).T
sort_df_numpy=sort_df.to_numpy().T    
sns.heatmap(sort_df_numpy[:30,:], annot=True, cmap="YlGnBu", xticklabels=["Factor1", "Factor2"], yticklabels=sort_df.columns[:30])
plt.title("因子载荷热力图")
plt.xlabel("Factors")
plt.ylabel("Variables")

# 因子得分散点图
plt.subplot(1, 2, 2)
plt.scatter(factor_scores[:, 0], factor_scores[:, 1], c="tomato", alpha=0.7, edgecolor="k")
plt.axhline(0, color="black", linestyle="--", linewidth=0.8)
plt.axvline(0, color="black", linestyle="--", linewidth=0.8)
plt.title("因子得分散点图")
plt.xlabel("Factor 1")
plt.ylabel("Factor 2")

plt.tight_layout()
plt.show()

FactorAnalysis(n_components=6, random_state=42)

FactorAnalysis(n_components=6, random_state=42)

<Figure size 1200x600 with 0 Axes>

<Axes: >

<Axes: >

Text(0.5, 1.0, '因子载荷热力图')

Text(0.5, 38.72222222222221, 'Factors')

Text(122.72222222222221, 0.5, 'Variables')

<Axes: >

<matplotlib.collections.PathCollection at 0x1959059e340>

Communication_Services= ['GOOGL', 'GOOG', 'T', 'CHTR', 'CMCSA', 'EA', 'FOXA', 'FOX', 'IPG', 'LYV', 'MTCH', 'META', 'NFLX', 'NWSA', 'NWS', 'OMC', 'PARA',
                         'TMUS', 'TTWO', 'VZ', 'DIS', 'WBD']
Consumer_Discretionary= ['ABNB', 'AMZN', 'APTV', 'BBY', 'BWA', 'CZR', 'KMX', 'CCL', 'CMG', 'DHI', 'DRI', 'DECK', 'DPZ', 'EBAY', 'EXPE', 'F', 'GRMN',
                         'GM', 'GPC', 'HAS', 'HLT', 'HD', 'LVS', 'LEN', 'LKQ', 'LOW', 'LULU', 'MAR', 'MCD', 'MGM', 'MHK', 'NKE', 'NCLH', 'ORLY', 'PHM', 'RL', 
                         'ROST', 'RCL', 'SBUX', 'TPR', 'TSLA', 'TJX', 'TSCO', 'ULTA', 'WYNN', 'YUM']
Consumer_Staples=['MO', 'ADM', 'BG', 'CPB', 'CHD', 'CLX', 'KO', 'CL', 'CAG', 'STZ', 'COST', 'DG', 'DLTR', 'EL', 'GIS', 'HSY', 'HRL', 'SJM', 'K', 'KVUE', 'KDP', 
                  'KMB', 'KHC', 'KR', 'LW', 'MKC', 'TAP', 'MDLZ', 'MNST', 'PEP', 'PM', 'PG', 'SYY', 'TGT', 'TSN', 'WBA', 'WMT']
Energy=['APA', 'BKR', 'CVX', 'COP', 'CTRA', 'DVN', 'FANG', 'EOG', 'EQT', 'XOM', 'HAL', 'HES', 'KMI', 'MPC', 'OXY', 'OKE', 'PSX', 'SLB', 'TRGP', 'VLO', 'WMB']
Financials=['AFL', 'ALL', 'AXP', 'AIG', 'AMP', 'AON', 'ACGL', 'AJG', 'BAC', 'BLK', 'BX', 'BK', 'BRO', 'COF', 'CBOE', 'SCHW', 'CB', 'C', 'CFG', 'CME', 'CPAY', 
            'DFS', 'FIS', 'FITB', 'FI', 'BEN', 'GPN', 'GL', 'GS', 'HIG', 'HBAN', 'ICE', 'IVZ', 'JKHY', 'JPM', 'KEY', 'KKR', 'L', 'MTB', 'MKTX', 'MMC', 'MA', 'MET',
            'MCO', 'MS', 'MSCI', 'NDAQ', 'NTRS', 'PYPL', 'PNC', 'PFG', 'PGR', 'PRU', 'RJF', 'RF', 'SPGI', 'STT', 'SYF', 'TROW', 'TRV', 'TFC', 'USB', 'V', 'WRB', 'WFC', 'WTW']
Health_Care=['ABT', 'ABBV', 'A', 'ALGN', 'AMGN', 'BAX', 'BDX', 'TECH', 'BIIB', 'BSX', 'BMY', 'CAH', 'CTLT', 'COR', 'CNC', 'CRL', 'CI', 'COO', 'CVS', 'DHR', 'DVA', 
             'DXCM', 'EW', 'ELV', 'GEHC', 'GILD', 'HCA', 'HSIC', 'HOLX', 'HUM', 'IDXX', 'INCY', 'PODD', 'ISRG', 'IQV', 'JNJ', 'LH', 'LLY', 'MCK', 'MDT', 'MRK', 
             'MRNA', 'MOH', 'PFE', 'DGX', 'REGN', 'RMD', 'RVTY', 'SOLV', 'STE', 'SYK', 'TFX', 'TMO', 'UNH', 'UHS', 'VRTX', 'VTRS', 'WAT', 'WST', 'ZBH', 'ZTS']
Industrials=['MMM', 'AOS', 'ALLE', 'AMTM', 'AME', 'ADP', 'AXON', 'BA', 'BLDR', 'CHRW', 'CARR', 'CAT', 'CTAS', 'CPRT', 'CSX', 'CMI', 'DAY', 'DE', 'DAL', 'DOV', 
             'ETN', 'EMR', 'EFX', 'EXPD', 'FAST', 'FDX', 'FTV', 'GE', 'GEV', 'GNRC', 'GD', 'HON', 'HWM', 'HII', 'IEX', 'ITW', 'IR', 'J', 'JCI', 'LHX', 'LDOS', 
             'LMT', 'MAS', 'NSC', 'NOC', 'ODFL', 'OTIS', 'PCAR', 'PH', 'PAYX', 'PAYC', 'PNR', 'PWR', 'RSG', 'ROK', 'ROL', 'RTX', 'LUV', 'SWK', 'TXT', 'TT', 'TDG', 
             'UBER', 'UNP', 'UAL', 'UPS', 'URI', 'VLTO', 'VRSK', 'WAB', 'WM', 'XYL']
Information_Technology=[ 'ACN', 'ADBE', 'AMD', 'AKAM', 'APH', 'ADI', 'ANSS', 'AAPL', 'AMAT', 'ANET', 'ADSK', 'AVGO', 'CDNS', 'CDW', 'CSCO', 'CTSH', 'GLW', 'CRWD',
                        'DELL', 'ENPH', 'EPAM', 'FFIV', 'FSLR', 'FTNT', 'IT', 'GEN', 'GDDY', 'HPE', 'HPQ', 'IBM', 'INTC', 'INTU', 'JBL', 'JNPR', 'KEYS', 'KLAC', 
                        'LRCX', 'MCHP', 'MU', 'MSFT', 'MPWR', 'MSI', 'NTAP', 'NVDA', 'NXPI', 'ON', 'ORCL', 'PLTR', 'PANW', 'PTC', 'QRVO', 'QCOM', 'ROP', 'CRM', 
                        'STX', 'NOW', 'SWKS', 'SMCI', 'SNPS', 'TEL', 'TDY', 'TER', 'TXN', 'TRMB', 'VRSN', 'WDC', 'ZBRA']
Materials=['APD', 'ALB', 'AMCR', 'AVY', 'BALL', 'CE', 'CF', 'CTVA', 'DOW', 'DD', 'EMN', 'ECL', 'FMC', 'FCX', 'IFF', 'IP', 'LIN', 'LYB', 'MLM', 'MOS', 'NEM', 'NUE',
           'PKG', 'PPG', 'SHW', 'SW', 'STLD', 'VMC']
Real_Estate=['ARE', 'AMT', 'AVB', 'BXP', 'CPT', 'CBRE', 'CSGP', 'CCI', 'DLR', 'EQIX', 'EQR', 'ESS', 'EXR', 'FRT', 'DOC', 'HST', 'INVH', 'IRM', 'KIM', 'MAA', 'PLD', 
             'PSA', 'O', 'REG', 'SBAC', 'SPG', 'UDR', 'VTR', 'VICI', 'WELL', 'WY']
Utilities=['AES', 'LNT', 'AEE', 'AEP', 'AWK', 'ATO', 'CNP', 'CMS', 'ED', 'CEG', 'D', 'DTE', 'DUK', 'EIX', 'ETR', 'EVRG', 'ES', 'EXC', 'FE', 'NEE', 'NI', 'NRG',
           'PCG', 'PNW', 'PPL', 'PEG', 'SRE', 'SO', 'VST', 'WEC', 'XEL']
Industry={'Communication_Services':Communication_Services,'Consumer_Discretionary':Consumer_Discretionary,
          'Consumer_Staples':Consumer_Staples,'Energy':Energy, 
          'Financials':Financials,'Health_Care':Health_Care,'Industrials':Industrials,
          'Information_Technology':Information_Technology,'Materials':Materials,
          'Real_Estate':Real_Estate,'Utilities':Utilities}
industry_dict=Industry
# 计算最长的列表长度
max_length = max(len(lst) for lst in industry_dict.values())

# 填充 NaN 以使所有列表长度相同
for key in industry_dict:
    industry_dict[key] += [np.nan] * (max_length - len(industry_dict[key]))

# 转换为 DataFrame
df_industries = pd.DataFrame(industry_dict)
# 函数：根据公司名称查找行业
def find_company_industry(company_name, industry_dict):
    for industry, companies in industry_dict.items():
        if company_name in companies:
            return industry
    return None



#因子1的行业占比
sort_df = pd.DataFrame(factor_loadings.T,columns=columns ).T
sort_df=sort_df.sort_values(by=[0,1], ascending=[False,False]).T
sort_df_numpy=sort_df.to_numpy().T   
columns1=sort_df.columns[:30]

# 检索每个公司的行业
company_industry_map = {company: find_company_industry(company, industry_dict) for company in columns1}

# 输出结果
for company, industry in company_industry_map.items():
    print(f"公司 {company} 所在行业: {industry}")

公司 ATO 所在行业: Utilities
公司 CSX 所在行业: Industrials
公司 NSC 所在行业: Industrials
公司 CCI 所在行业: Real_Estate
公司 ED 所在行业: Utilities
公司 CI 所在行业: Health_Care
公司 PHM 所在行业: Consumer_Discretionary
公司 SO 所在行业: Utilities
公司 DHI 所在行业: Consumer_Discretionary
公司 LEN 所在行业: Consumer_Discretionary
公司 CARR 所在行业: Industrials
公司 CVS 所在行业: Health_Care
公司 LNT 所在行业: Utilities
公司 FE 所在行业: Utilities
公司 HAL 所在行业: Energy
公司 ODFL 所在行业: Industrials
公司 GNRC 所在行业: Industrials
公司 HOLX 所在行业: Health_Care
公司 WEC 所在行业: Utilities
公司 DTE 所在行业: Utilities
公司 BKR 所在行业: Energy
公司 SLB 所在行业: Energy
公司 MAA 所在行业: Real_Estate
公司 CTVA 所在行业: Materials
公司 MDT 所在行业: Health_Care
公司 CPAY 所在行业: Financials
公司 SRE 所在行业: Utilities
公司 HCA 所在行业: Health_Care
公司 NUE 所在行业: Materials
公司 LMT 所在行业: Industrials

from sklearn.decomposition import FastICA

# 数据准备
X = x_data.to_numpy()  # 观测信号
time=np.arange(len(X))

#  应用 ICA
ica = FastICA(n_components=2, random_state=42)
S_estimated = ica.fit_transform(X)  # 分离出的信号
A_estimated = ica.mixing_  # 估计的混合矩阵

# 绘图分析
fig, axes = plt.subplots(2, 2, figsize=(12, 8), constrained_layout=True)


# 混合信号
axes[0, 0].plot(time, X[:, 0], color='green')
axes[0, 0].set_title('股票A')
axes[0, 1].plot(time, X[:, 99], color='purple')
axes[0, 1].set_title('股票B')

# 分离信号
axes[1, 0].plot(time, S_estimated[:, 0], color='orange')
axes[1, 0].set_title('提取特征A')
axes[1, 1].plot(time, S_estimated[:, 1], color='cyan')
axes[1, 1].set_title('提取特征B')

plt.suptitle('Independent Component Analysis (ICA) Results', fontsize=16)
plt.show()

[<matplotlib.lines.Line2D at 0x195904fb100>]

Text(0.5, 1.0, '股票A')

[<matplotlib.lines.Line2D at 0x195904fb4c0>]

Text(0.5, 1.0, '股票B')

[<matplotlib.lines.Line2D at 0x195904fb730>]

Text(0.5, 1.0, '提取特征A')

[<matplotlib.lines.Line2D at 0x195904fb9a0>]

Text(0.5, 1.0, '提取特征B')

Text(0.5, 0.98, 'Independent Component Analysis (ICA) Results')

from sklearn.manifold import MDS
from sklearn.metrics import pairwise_distances
data=x_data

distance_matrix = pairwise_distances(data, metric='euclidean')
# MDS降维
mds = MDS(n_components=6, dissimilarity='precomputed', random_state=42)
low_dim_data = mds.fit_transform(distance_matrix)

# 绘图
fig, ax = plt.subplots(1, 2, figsize=(16, 8), dpi=120)

# 图1：MDS降维后的散点图
scatter = ax[0].scatter(low_dim_data[:, 0], low_dim_data[:, 1], cmap='viridis', s=50, edgecolor='k')
ax[0].set_title("MDS Projection (2D)", fontsize=14)
ax[0].set_xlabel("Component 1")
ax[0].set_ylabel("Component 2")
plt.colorbar(scatter, ax=ax[0], label="Cluster Labels")

# 图2：距离矩阵的热力图
im = ax[1].imshow(distance_matrix, cmap='hot', interpolation='nearest')
ax[1].set_title("Distance Matrix Heatmap", fontsize=14)
ax[1].set_xlabel("Sample Index")
ax[1].set_ylabel("Sample Index")
plt.colorbar(im, ax=ax[1], label="Distance")

plt.tight_layout()
plt.show()

C:\Users\cqm\AppData\Local\Temp\ipykernel_30380\2286233253.py:14: UserWarning: No data for colormapping provided via 'c'. Parameters 'cmap' will be ignored
  scatter = ax[0].scatter(low_dim_data[:, 0], low_dim_data[:, 1], cmap='viridis', s=50, edgecolor='k')

Text(0.5, 1.0, 'MDS Projection (2D)')

Text(0.5, 0, 'Component 1')

Text(0, 0.5, 'Component 2')

<matplotlib.colorbar.Colorbar at 0x195b3ccd9d0>

Text(0.5, 1.0, 'Distance Matrix Heatmap')

Text(0.5, 0, 'Sample Index')

Text(0, 0.5, 'Sample Index')

<matplotlib.colorbar.Colorbar at 0x195b3d12100>

from sklearn.manifold import TSNE
from sklearn.decomposition import PCA

X=x_data

# 使用PCA降维到3D空间（便于对比）
pca = PCA(n_components=3)
X_pca1 = pca.fit_transform(X)

# 使用t-SNE降维到2D空间
tsne = TSNE(n_components=2, random_state=42, perplexity=30, n_iter=1000)
X_tsne = tsne.fit_transform(X)

fig = plt.figure(figsize=(16, 8))

# 原始PCA 3D降维
ax1 = fig.add_subplot(1, 2, 1, projection='3d')
scatter = ax1.scatter(X_pca1[:, 0], X_pca1[:, 1], X_pca1[:, 2], cmap='rainbow', s=10)
ax1.set_title('PCA 3D Visualization')
ax1.set_xlabel('PCA1')
ax1.set_ylabel('PCA2')
ax1.set_zlabel('PCA3')
legend1 = ax1.legend(*scatter.legend_elements(), title="Classes", loc="best")
ax1.add_artist(legend1)

# t-SNE 2D降维
ax2 = fig.add_subplot(1, 2, 2)
scatter = ax2.scatter(X_tsne[:, 0], X_tsne[:, 1], cmap='rainbow', s=10)
ax2.set_title('t-SNE 2D Visualization')
ax2.set_xlabel('t-SNE1')
ax2.set_ylabel('t-SNE2')
legend2 = ax2.legend(*scatter.legend_elements(), title="Classes", loc="best")
ax2.add_artist(legend2)

plt.tight_layout()
plt.show()

c:\anaconda\envs\pytorch\lib\site-packages\sklearn\manifold\_t_sne.py:1162: FutureWarning: 'n_iter' was renamed to 'max_iter' in version 1.5 and will be removed in 1.7.
  warnings.warn(
C:\Users\cqm\AppData\Local\Temp\ipykernel_30380\647746706.py:18: UserWarning: No data for colormapping provided via 'c'. Parameters 'cmap' will be ignored
  scatter = ax1.scatter(X_pca1[:, 0], X_pca1[:, 1], X_pca1[:, 2], cmap='rainbow', s=10)

Text(0.5, 0.92, 'PCA 3D Visualization')

Text(0.5, 0, 'PCA1')

Text(0.5, 0.5, 'PCA2')

Text(0.5, 0, 'PCA3')

c:\anaconda\envs\pytorch\lib\site-packages\matplotlib\collections.py:1109: UserWarning: Collection without array used. Make sure to specify the values to be colormapped via the `c` argument.
  warnings.warn("Collection without array used. Make sure to "

<matplotlib.legend.Legend at 0x195cdab8460>

C:\Users\cqm\AppData\Local\Temp\ipykernel_30380\647746706.py:28: UserWarning: No data for colormapping provided via 'c'. Parameters 'cmap' will be ignored
  scatter = ax2.scatter(X_tsne[:, 0], X_tsne[:, 1], cmap='rainbow', s=10)

Text(0.5, 1.0, 't-SNE 2D Visualization')

Text(0.5, 0, 't-SNE1')

import umap
# 第一步：生成数据集
X=x_data.to_numpy()

# 第二步：应用 UMAP 进行降维

reducer = umap.UMAP(n_neighbors=15, min_dist=0.1, n_components=2, random_state=42)
embedding = reducer.fit_transform(X)

# 第三步：可视化
fig, axs = plt.subplots(1, 2, figsize=(12, 6), dpi=120)

#  UMAP 2D 嵌入
scatter = axs[0].scatter(embedding[:, 0], embedding[:, 1],  cmap='Spectral', s=5)
axs[0].set_title("UMAP 2D Embedding")
axs[0].set_xlabel("UMAP1")
axs[0].set_ylabel("UMAP2")

# UMAP 嵌入的密度图
sns.kdeplot(x=embedding[:, 0], y=embedding[:, 1], cmap="Reds", fill=True, ax=axs[1])
axs[1].set_title("Density of UMAP Embedding")
axs[1].set_xlabel("UMAP1")
axs[1].set_ylabel("UMAP2")

# 为 UMAP 图添加颜色条
cbar = fig.colorbar(scatter, ax=axs[1], orientation='vertical', fraction=0.02, pad=0.04)
cbar.set_label("Color")

plt.tight_layout()
plt.show()

c:\anaconda\envs\pytorch\lib\site-packages\umap\umap_.py:1952: UserWarning: n_jobs value 1 overridden to 1 by setting random_state. Use no seed for parallelism.
  warn(
C:\Users\cqm\AppData\Local\Temp\ipykernel_30380\3946075921.py:14: UserWarning: No data for colormapping provided via 'c'. Parameters 'cmap' will be ignored
  scatter = axs[0].scatter(embedding[:, 0], embedding[:, 1],  cmap='Spectral', s=5)

Text(0.5, 1.0, 'UMAP 2D Embedding')

Text(0.5, 0, 'UMAP1')

Text(0, 0.5, 'UMAP2')

<Axes: >

Text(0.5, 1.0, 'Density of UMAP Embedding')

Text(0.5, 0, 'UMAP1')

Text(0, 0.5, 'UMAP2')

from sklearn.decomposition import KernelPCA


X=x_data.to_numpy()

# 核PCA降维
kernel_pca = KernelPCA(n_components=2, kernel='rbf', gamma=15,fit_inverse_transform=True)
X_kpca = kernel_pca.fit_transform(X)

#投影后数据可视化
plt.subplot(1, 2, 1)
plt.scatter(X_kpca[:, 0], X_kpca[:, 1], cmap='plasma', edgecolor='k')
plt.title('Kernel PCA Projection')
plt.xlabel('PC1')
plt.ylabel('PC2')

# 核PCA没有显式的解释方差，因此直接基于特征值来估计
lambdas = kernel_pca.eigenvalues_
explained_variance_ratio = lambdas / np.sum(lambdas)
cumulative_variance_ratio = np.cumsum(explained_variance_ratio)

plt.subplot(1, 2, 2)
plt.plot(range(1, len(cumulative_variance_ratio) + 1), cumulative_variance_ratio, marker='o', color='red')
plt.title('Cumulative Variance Ratio')
plt.xlabel('Number of Components')
plt.ylabel('Cumulative Variance')

# 总体展示
plt.tight_layout()
plt.show()

<Axes: >

C:\Users\cqm\AppData\Local\Temp\ipykernel_30380\2229412370.py:12: UserWarning: No data for colormapping provided via 'c'. Parameters 'cmap' will be ignored
  plt.scatter(X_kpca[:, 0], X_kpca[:, 1], cmap='plasma', edgecolor='k')

<matplotlib.collections.PathCollection at 0x195b4267310>

Text(0.5, 1.0, 'Kernel PCA Projection')

Text(0.5, 0, 'PC1')

Text(0, 0.5, 'PC2')

<Axes: >

[<matplotlib.lines.Line2D at 0x195b445e640>]

Text(0.5, 1.0, 'Cumulative Variance Ratio')

Text(0.5, 0, 'Number of Components')

import torch
import torch.nn as nn
import torch.optim as optim

data = torch.tensor(x_data.to_numpy(), dtype=torch.float32)

# 2. 定义自编码器
class Autoencoder(nn.Module):
    def __init__(self, input_dim, latent_dim):
        super(Autoencoder, self).__init__()
        # 编码器
        self.encoder = nn.Sequential(
            nn.Linear(input_dim, 8),
            nn.ReLU(),
            nn.Linear(8, latent_dim),
        )
        # 解码器
        self.decoder = nn.Sequential(
            nn.Linear(latent_dim, 8),
            nn.ReLU(),
            nn.Linear(8, input_dim),
        )
    
    def forward(self, x):
        z = self.encoder(x)
        x_hat = self.decoder(z)
        return x_hat, z

# 3. 初始化模型
input_dim = 482
latent_dim = 2
model = Autoencoder(input_dim, latent_dim)
criterion = nn.MSELoss()
optimizer = optim.Adam(model.parameters(), lr=0.01)

# 4. 训练模型
epochs = 100
losses = []

for epoch in range(epochs):
    model.train()
    optimizer.zero_grad()
    x_hat, z = model(data)
    loss = criterion(x_hat, data)
    loss.backward()
    optimizer.step()
    losses.append(loss.item())
    if (epoch + 1) % 10 == 0:
        print(f"Epoch {epoch+1}/{epochs}, Loss: {loss.item():.4f}")

# 5. 可视化分析
model.eval()
with torch.no_grad():
    x_hat, z = model(data)

# 创建子图
fig, axs = plt.subplots(1, 2, figsize=(12, 6))

# 图1：原始数据 vs 重建数据
axs[0].scatter(data[:, 0], data[:, 99], color='blue', alpha=0.5, label='Original Data')
axs[0].scatter(x_hat[:, 0], x_hat[:, 99], color='red', alpha=0.5, label='Reconstructed Data')
axs[0].set_title('原始数据和重构后的数据')
axs[0].legend()
axs[0].grid(False)

# 图2：潜在空间分布
axs[1].scatter(z[:, 0], z[:, 1], color='green', alpha=0.7)
axs[1].set_title('潜在空间分布')
axs[1].grid(False)

plt.tight_layout()
plt.show()

Autoencoder(
  (encoder): Sequential(
    (0): Linear(in_features=482, out_features=8, bias=True)
    (1): ReLU()
    (2): Linear(in_features=8, out_features=2, bias=True)
  )
  (decoder): Sequential(
    (0): Linear(in_features=2, out_features=8, bias=True)
    (1): ReLU()
    (2): Linear(in_features=8, out_features=482, bias=True)
  )
)

Autoencoder(
  (encoder): Sequential(
    (0): Linear(in_features=482, out_features=8, bias=True)
    (1): ReLU()
    (2): Linear(in_features=8, out_features=2, bias=True)
  )
  (decoder): Sequential(
    (0): Linear(in_features=2, out_features=8, bias=True)
    (1): ReLU()
    (2): Linear(in_features=8, out_features=482, bias=True)
  )
)

Autoencoder(
  (encoder): Sequential(
    (0): Linear(in_features=482, out_features=8, bias=True)
    (1): ReLU()
    (2): Linear(in_features=8, out_features=2, bias=True)
  )
  (decoder): Sequential(
    (0): Linear(in_features=2, out_features=8, bias=True)
    (1): ReLU()
    (2): Linear(in_features=8, out_features=482, bias=True)
  )
)

Autoencoder(
  (encoder): Sequential(
    (0): Linear(in_features=482, out_features=8, bias=True)
    (1): ReLU()
    (2): Linear(in_features=8, out_features=2, bias=True)
  )
  (decoder): Sequential(
    (0): Linear(in_features=2, out_features=8, bias=True)
    (1): ReLU()
    (2): Linear(in_features=8, out_features=482, bias=True)
  )
)

Autoencoder(
  (encoder): Sequential(
    (0): Linear(in_features=482, out_features=8, bias=True)
    (1): ReLU()
    (2): Linear(in_features=8, out_features=2, bias=True)
  )
  (decoder): Sequential(
    (0): Linear(in_features=2, out_features=8, bias=True)
    (1): ReLU()
    (2): Linear(in_features=8, out_features=482, bias=True)
  )
)

Autoencoder(
  (encoder): Sequential(
    (0): Linear(in_features=482, out_features=8, bias=True)
    (1): ReLU()
    (2): Linear(in_features=8, out_features=2, bias=True)
  )
  (decoder): Sequential(
    (0): Linear(in_features=2, out_features=8, bias=True)
    (1): ReLU()
    (2): Linear(in_features=8, out_features=482, bias=True)
  )
)

Autoencoder(
  (encoder): Sequential(
    (0): Linear(in_features=482, out_features=8, bias=True)
    (1): ReLU()
    (2): Linear(in_features=8, out_features=2, bias=True)
  )
  (decoder): Sequential(
    (0): Linear(in_features=2, out_features=8, bias=True)
    (1): ReLU()
    (2): Linear(in_features=8, out_features=482, bias=True)
  )
)

Autoencoder(
  (encoder): Sequential(
    (0): Linear(in_features=482, out_features=8, bias=True)
    (1): ReLU()
    (2): Linear(in_features=8, out_features=2, bias=True)
  )
  (decoder): Sequential(
    (0): Linear(in_features=2, out_features=8, bias=True)
    (1): ReLU()
    (2): Linear(in_features=8, out_features=482, bias=True)
  )
)

Autoencoder(
  (encoder): Sequential(
    (0): Linear(in_features=482, out_features=8, bias=True)
    (1): ReLU()
    (2): Linear(in_features=8, out_features=2, bias=True)
  )
  (decoder): Sequential(
    (0): Linear(in_features=2, out_features=8, bias=True)
    (1): ReLU()
    (2): Linear(in_features=8, out_features=482, bias=True)
  )
)

Autoencoder(
  (encoder): Sequential(
    (0): Linear(in_features=482, out_features=8, bias=True)
    (1): ReLU()
    (2): Linear(in_features=8, out_features=2, bias=True)
  )
  (decoder): Sequential(
    (0): Linear(in_features=2, out_features=8, bias=True)
    (1): ReLU()
    (2): Linear(in_features=8, out_features=482, bias=True)
  )
)

z.shape

torch.Size([2340, 2])

def reduction_xicor(x,y):
    x=np.array(x);y=np.array(y)
    p=x.shape[1];rho=[]
    for i in range(p):
        rho.append(max(Xi(list(x[:,i]),list(y)).correlation,Xi(list(y),list(x[:,i])).correlation))
    return rho

def reduction_pearsonr(x,y):
    x=np.array(x);y=np.array(y)
    p=x.shape[1];rho=[]
    for i in range(p):
        rho.append(pearsonr(x[:,i],y)[0])
    return rho

reduction_xicor(X_pca,y_data)

[0.7459004048727824,
 0.7481674245395772,
 0.5584143721635395,
 0.4331119547901775,
 0.30003493681695825,
 0.4064567182512817]

reduction_pearsonr(X_pca,y_data)

[0.7083096789491002,
 -0.6320078786457969,
 -0.037307291010294424,
 0.0923318900143941,
 0.14906052044247192,
 0.19183080659713656]

reduction_xicor(factor_scores,y_data)

[0.7484501171804825,
 0.7617224271001951,
 0.5827116950785585,
 0.5674030120072084,
 0.38946990871553455,
 0.3844826839949381]

reduction_pearsonr(factor_scores,y_data)

[-0.7343696011917709,
 -0.6092612746411366,
 0.0542417977173028,
 -0.0623710314881693,
 -0.12528733045690876,
 0.18332668381712192]

ica = FastICA(n_components=6, random_state=42)
S_estimated1 = ica.fit_transform(X)  # 分离出的信号
reduction_xicor(S_estimated1,y_data)

[0.4414496021348532,
 0.42401534517045536,
 0.3039451939413387,
 0.7065951707078415,
 0.5546470806207686,
 0.3306891173002259]

reduction_pearsonr(S_estimated1,y_data)

[0.2972723875824521,
 0.07324544942087362,
 0.38351719475898216,
 -0.8161480348066641,
 -0.18469031486676912,
 0.1704181486629671]

reduction_xicor(low_dim_data,y_data)

[0.5367208226899011,
 0.4674407311419262,
 0.4466205432501539,
 0.7051943081442855,
 0.450000995324895,
 0.340893480329732]

reduction_pearsonr(low_dim_data,y_data)

[0.6005599523194682,
 0.13558474452281036,
 -0.07688185949302231,
 -0.8578777562439068,
 -0.07554015165043973,
 0.02540276577731806]

tsne1 = TSNE(n_components=3, random_state=42, perplexity=30, n_iter=1000)
X_tsne1 = tsne1.fit_transform(X)
reduction_xicor(X_tsne1,y_data)

c:\anaconda\envs\pytorch\lib\site-packages\sklearn\manifold\_t_sne.py:1162: FutureWarning: 'n_iter' was renamed to 'max_iter' in version 1.5 and will be removed in 1.7.
  warnings.warn(

[0.48284178589410953, 0.46828611810324317, 0.36653752565520215]

reduction_pearsonr(X_tsne1,y_data)

[0.6122914509078293, -0.4863056001563527, 0.006704770922268464]

reducer1 = umap.UMAP(n_neighbors=15, min_dist=0.1, n_components=6, random_state=42)
embedding1 = reducer1.fit_transform(X)
reduction_xicor(embedding1,y_data)

c:\anaconda\envs\pytorch\lib\site-packages\umap\umap_.py:1952: UserWarning: n_jobs value 1 overridden to 1 by setting random_state. Use no seed for parallelism.
  warn(

[0.758938233299651,
 0.4563471503300368,
 0.38572309623111556,
 0.34759302132972125,
 0.34411504567810747,
 0.34324007291257097]

reduction_pearsonr(embedding1,y_data)

[-0.6084088004336915,
 -0.15193324811513242,
 0.1299335100577593,
 -0.020454157224254456,
 0.16963724734130026,
 -0.10434447647008584]

kernel_pca1 = KernelPCA(n_components=6, kernel='rbf', gamma=15,fit_inverse_transform=True)
X_kpca1 = kernel_pca1.fit_transform(X)
reduction_xicor(X_kpca1,y_data)

[0.26596907307594597,
 0.2773929809280544,
 0.27674134160613006,
 0.2846975720741751,
 0.2618489896450399,
 0.2733491096369587]

reduction_pearsonr(X_kpca1,y_data)

[-0.034943145721764504,
 -0.03150887538542018,
 0.025142330088421656,
 -0.02199287558944993,
 -0.024738561667554088,
 -0.043182417360195686]

reduction_xicor(z,y_data)

[0.6328036257682754,
 0.6473454319792227,
 0.6354453775404563,
 0.7953190230515058,
 0.6747451331658447,
 0.7394576423591268]

reduction_pearsonr(z,y_data)

[0.4464784643900447,
 0.7340306549811457,
 0.7267903125083403,
 -0.7457705131219041,
 -0.7375254950328844,
 0.8882634058457526]

#导出依赖包
import pipreqs
!pipreqs  --encoding=utf8

INFO: Not scanning for jupyter notebooks.
WARNING: Import named "matplotlib" not found locally. Trying to resolve it at the PyPI server.
WARNING: Import named "matplotlib" was resolved to "matplotlib:3.10.0" package (https://pypi.org/project/matplotlib/).
Please, verify manually the final list of requirements.txt to avoid possible dependency confusions.
WARNING: Import named "numpy" not found locally. Trying to resolve it at the PyPI server.
WARNING: Import named "numpy" was resolved to "numpy:2.2.1" package (https://pypi.org/project/numpy/).
Please, verify manually the final list of requirements.txt to avoid possible dependency confusions.
WARNING: Import named "pandas" not found locally. Trying to resolve it at the PyPI server.
WARNING: Import named "pandas" was resolved to "pandas:2.2.3" package (https://pypi.org/project/pandas/).
Please, verify manually the final list of requirements.txt to avoid possible dependency confusions.
WARNING: Import named "scikit_learn" not found locally. Trying to resolve it at the PyPI server.
WARNING: Import named "scikit_learn" was resolved to "scikit-learn:1.6.0" package (https://pypi.org/project/scikit-learn/).
Please, verify manually the final list of requirements.txt to avoid possible dependency confusions.
WARNING: Import named "scipy" not found locally. Trying to resolve it at the PyPI server.
WARNING: Import named "scipy" was resolved to "scipy:1.14.1" package (https://pypi.org/project/scipy/).
Please, verify manually the final list of requirements.txt to avoid possible dependency confusions.
WARNING: Import named "seaborn" not found locally. Trying to resolve it at the PyPI server.
WARNING: Import named "seaborn" was resolved to "seaborn:0.13.2" package (https://pypi.org/project/seaborn/).
Please, verify manually the final list of requirements.txt to avoid possible dependency confusions.
WARNING: Import named "yfinance" not found locally. Trying to resolve it at the PyPI server.
WARNING: Import named "yfinance" was resolved to "yfinance:0.2.51" package (https://pypi.org/project/yfinance/).
Please, verify manually the final list of requirements.txt to avoid possible dependency confusions.
INFO: Successfully saved requirements file in c:\Users\cqm\Desktop\多元统计陈麒名\requirements.txt

	SPY	GOOGL	GOOG	T	CHTR	CMCSA	EA	FOXA	FOX	IPG	LYV	MTCH	META	NFLX	NWSA	NWS	OMC	PARA	TMUS	TTWO	VZ	DIS	WBD	ABNB	AMZN	APTV	BBY	BWA	CZR	KMX	CCL	CMG	DHI	DRI	DECK	DPZ	EBAY	EXPE	F	GRMN	GM	GPC	HAS	HLT	HD	LVS	LEN	LKQ	LOW	LULU	MAR	MCD	MGM	MHK	NKE	NCLH	ORLY	PHM	RL	ROST	RCL	SBUX	TPR	TSLA	TJX	TSCO	ULTA	WYNN	YUM	MO	ADM	BG	CPB	CHD	CLX	KO	CL	CAG	STZ	COST	DG	DLTR	EL	GIS	HSY	HRL	SJM	K	KVUE	KDP	KMB	KHC	KR	LW	MKC	TAP	MDLZ	MNST	PEP	PM	PG	SYY	TGT	TSN	WBA	WMT	APA	BKR	CVX	COP	CTRA	DVN	FANG	EOG	EQT	XOM	HAL	HES	KMI	MPC	OXY	OKE	PSX	SLB	TRGP	VLO	WMB	AFL	ALL	AXP	AIG	AMP	AON	ACGL	AJG	BAC	BLK	BX	BK	BRO	COF	CBOE	SCHW	CB	C	CFG	CME	CPAY	DFS	FIS	FITB	FI	BEN	GPN	GL	GS	HIG	HBAN	ICE	IVZ	JKHY	JPM	KEY	KKR	L	MTB	MKTX	MMC	MA	MET	MCO	MS	MSCI	NDAQ	NTRS	PYPL	PNC	PFG	PGR	PRU	RJF	RF	SPGI	STT	SYF	TROW	TRV	TFC	USB	V	WRB	WFC	WTW	ABT	ABBV	A	ALGN	AMGN	BAX	BDX	TECH	BIIB	BSX	BMY	CAH	CTLT	COR	CNC	CRL	CI	COO	CVS	DHR	DVA	DXCM	EW	ELV	GEHC	GILD	HCA	HSIC	HOLX	HUM	IDXX	INCY	PODD	ISRG	IQV	JNJ	LH	LLY	MCK	MDT	MRK	MRNA	MOH	PFE	DGX	REGN	RMD	RVTY	SOLV	STE	SYK	TFX	TMO	UNH	UHS	VRTX	VTRS	WAT	WST	ZBH	ZTS	MMM	AOS	ALLE	AMTM	AME	ADP	AXON	BA	BLDR	CHRW	CARR	CAT	CTAS	CPRT	CSX	CMI	DAY	DE	DAL	DOV	ETN	EMR	EFX	EXPD	FAST	FDX	FTV	GE	GEV	GNRC	GD	HON	HWM	HII	IEX	ITW	IR	J	JCI	LHX	LDOS	LMT	MAS	NSC	NOC	ODFL	OTIS	PCAR	PH	PAYX	PAYC	PNR	PWR	RSG	ROK	ROL	RTX	LUV	SWK	TXT	TT	TDG	UBER	UNP	UAL	UPS	URI	VLTO	VRSK	WAB	WM	XYL	ACN	ADBE	AMD	AKAM	APH	ADI	ANSS	AAPL	AMAT	ANET	ADSK	AVGO	CDNS	CDW	CSCO	CTSH	GLW	CRWD	DELL	ENPH	EPAM	FFIV	FSLR	FTNT	IT	GEN	GDDY	HPE	HPQ	IBM	INTC	INTU	JBL	JNPR	KEYS	KLAC	LRCX	MCHP	MU	MSFT	MPWR	MSI	NTAP	NVDA	NXPI	ON	ORCL	PLTR	PANW	PTC	QRVO	QCOM	ROP	CRM	STX	NOW	SWKS	SMCI	SNPS	TEL	TDY	TER	TXN	TRMB	VRSN	WDC	ZBRA	APD	ALB	AMCR	AVY	BALL	CE	CF	CTVA	DOW	DD	EMN	ECL	FMC	FCX	IFF	IP	LIN	LYB	MLM	MOS	NEM	NUE	PKG	PPG	SHW	SW	STLD	VMC	ARE	AMT	AVB	BXP	CPT	CBRE	CSGP	CCI	DLR	EQIX	EQR	ESS	EXR	FRT	DOC	HST	INVH	IRM	KIM	MAA	PLD	PSA	O	REG	SBAC	SPG	UDR	VTR	VICI	WELL	WY	AES	LNT	AEE	AEP	AWK	ATO	CNP	CMS	ED	CEG	D	DTE	DUK	EIX	ETR	EVRG	ES	EXC	FE	NEE	NI	NRG	PCG	PNW	PPL	PEG	SRE	SO	VST	WEC	XEL
0	-1.22	-2.68	-2.64	-1.22	-0.07	0.53	-2.11	2.24	2.24	0.80	1.09	-1.10	-3.01	-2.19	-1.40	-2.09	0.78	-0.81	1.11	-0.43	1.90	2.33	-1.53	-0.91	-1.37	-1.39	0.74	0.19	0.79	-0.53	-1.59	-1.00	1.79	2.78	-1.57	3.02	-0.51	-1.35	2.50	-0.77	2.20	0.89	-0.39	0.11	0.42	-1.26	1.65	-0.41	0.39	-1.15	0.01	-0.92	1.81	2.07	-0.52	0.06	-0.45	1.56	-0.95	-0.76	-0.47	1.64	-1.09	-0.82	0.64	-0.55	-1.24	-0.09	0.45	1.70	1.66	1.52	1.42	1.83	-0.49	1.85	1.53	-0.97	0.67	-1.92	-1.64	-1.58	-1.97	0.06	-0.56	0.07	0.60	1.61	1.72	-0.20	1.60	1.25	1.19	-1.39	0.28	1.12	1.25	1.33	1.89	1.47	1.53	-1.74	0.04	1.24	0.82	-1.22	1.45	1.91	1.63	2.97	2.60	1.76	1.68	2.54	1.65	1.56	1.52	1.41	2.22	1.19	1.56	2.53	0.97	1.47	2.90	1.33	2.89	3.17	2.56	2.33	2.47	2.74	1.99	2.01	1.69	2.79	-0.52	4.31	1.87	1.42	4.95	1.29	2.55	1.38	-1.06	3.28	-0.45	1.72	4.92	1.30	2.32	1.80	0.95	1.33	2.11	3.12	1.87	2.66	4.34	0.66	2.17	3.32	3.66	2.48	1.98	2.55	1.19	1.26	2.37	2.29	2.37	2.24	-1.13	2.87	2.32	-0.46	3.04	2.21	1.66	2.17	2.50	3.00	0.97	0.74	0.93	-0.56	1.69	2.65	3.09	1.96	2.54	3.58	-0.52	2.98	1.43	-0.94	-0.64	1.96	1.29	0.03	0.24	-0.07	0.62	0.67	-0.17	-2.96	1.09	1.40	0.47	1.19	0.88	1.30	0.90	2.06	-1.11	-1.14	0.97	0.77	-0.06	0.75	1.61	1.98	1.78	-1.15	0.38	-0.14	-0.04	-0.60	1.61	1.13	-1.31	1.26	1.32	-0.71	-0.16	-0.80	0.54	1.39	-1.04	1.80	-0.50	1.11	1.43	1.66	1.42	0.10	0.96	1.55	0.72	1.17	-0.73	2.36	1.43	-0.95	1.03	1.72	1.61	1.36	0.68	1.38	-0.87	-0.23	1.59	-0.77	2.32	2.91	0.88	2.22	1.62	-0.96	-0.10	1.45	-0.04	2.81	1.63	0.40	0.07	0.67	2.04	2.92	1.49	0.99	-0.26	1.93	2.95	3.02	0.12	2.67	0.84	2.36	1.04	1.99	0.91	1.83	1.36	2.64	-0.94	1.87	1.58	1.67	2.41	0.03	2.03	1.18	-0.25	1.90	1.67	2.24	-0.31	2.09	2.77	-1.95	1.72	1.34	0.68	-0.53	0.78	3.07	-0.67	2.78	0.65	2.31	1.60	-0.62	1.72	-0.75	0.88	-1.36	-0.52	-3.58	-1.88	-0.29	0.25	-1.96	-0.36	-1.68	-2.10	-1.64	-1.14	-2.14	-0.59	-0.94	-0.90	-1.98	0.56	-0.63	0.20	-1.60	0.76	-0.87	0.19	-1.09	-0.92	-1.03	-2.12	-1.24	2.09	-1.14	1.21	-0.49	-2.05	-1.03	-2.52	1.23	-2.43	-2.59	-1.62	0.85	-1.79	-1.07	0.81	0.95	-0.47	-1.36	-1.43	-1.95	-0.32	-1.42	0.62	-1.22	1.63	-1.36	-0.34	-2.51	0.35	-0.43	2.60	-1.96	0.93	-2.11	-0.84	1.90	0.33	1.53	0.35	1.69	1.57	0.89	0.79	-0.35	1.24	1.39	1.12	2.44	0.21	-0.00	1.28	2.69	1.26	1.50	1.63	2.61	0.01	0.32	1.36	1.73	-1.17	1.69	1.79	1.58	1.08	1.70	0.38	2.61	1.68	2.94	2.40	1.38	1.55	2.52	0.51	2.76	3.07	2.25	4.89	2.42	-0.83	2.50	1.54	2.75	1.95	1.20	2.30	4.29	3.54	1.18	1.66	3.32	2.51	3.35	2.90	1.47	-1.14	2.54	3.33	2.86	2.03	2.27	1.92	2.53	2.67	1.40	2.76	2.64	2.62	3.21	2.45	3.64	2.27	4.48	2.91	3.28	3.37	1.29	0.35	3.23	2.01	2.54	2.25	2.51	1.27	2.66	2.16
1	-1.31	-2.26	-2.25	-1.80	-0.23	0.51	-2.41	1.79	1.87	0.59	1.35	-0.59	-2.71	-2.08	-1.18	-1.94	0.76	-0.67	1.03	-0.97	1.57	2.75	-1.21	-0.52	-1.23	-1.24	0.23	0.15	0.45	-0.78	-0.93	-1.00	1.63	2.60	-2.02	2.23	-0.84	-1.20	2.40	-0.75	2.14	0.86	-0.44	0.23	-0.43	-0.66	1.46	-0.52	-0.39	-1.00	0.05	-1.01	1.48	2.33	-0.85	0.69	-0.45	1.52	-1.04	-0.72	-0.33	1.63	-1.15	-0.73	0.40	-1.16	-1.41	-0.20	-0.54	1.32	1.75	1.43	1.52	1.25	-0.75	1.96	1.29	-0.69	0.75	-2.03	-1.66	-1.63	-2.01	0.22	-0.54	0.06	0.43	0.95	1.48	-0.27	1.39	0.99	1.07	-1.49	0.03	1.14	1.29	1.60	1.80	1.27	1.29	-1.64	-0.13	0.95	1.35	-1.16	1.47	1.66	1.58	2.78	2.53	1.86	1.90	2.44	1.33	1.62	1.53	1.47	1.93	1.26	1.72	2.44	0.86	1.46	2.78	1.21	2.65	3.11	1.99	2.44	2.30	2.10	1.59	1.83	1.47	2.56	-0.70	3.46	1.77	1.45	4.39	1.11	2.36	1.22	-1.29	3.03	-0.75	1.64	4.57	0.85	2.32	1.74	1.08	1.32	1.75	3.03	1.68	2.45	4.38	0.46	1.98	2.74	3.47	2.48	1.92	2.35	1.22	1.12	1.62	2.21	1.89	2.49	-2.04	2.52	1.99	-0.43	2.61	2.46	1.50	2.08	2.47	2.59	0.73	0.65	0.61	-0.91	1.51	2.13	2.72	1.39	2.03	2.90	-0.65	2.84	1.32	-1.21	-1.12	1.79	1.27	-0.08	-0.38	0.26	0.77	0.54	-0.44	-2.54	0.93	1.41	0.67	1.18	0.84	1.24	0.94	1.79	-1.09	-1.15	1.00	0.68	0.10	0.70	1.61	1.88	1.79	-1.36	0.37	-0.17	-0.11	-0.09	1.60	1.19	-1.50	1.14	1.42	-0.96	-0.09	-1.05	0.50	1.24	-0.90	1.73	-0.62	1.07	1.32	1.67	1.18	0.30	0.94	1.48	0.60	1.11	-1.10	1.57	0.98	-1.07	0.97	1.45	0.68	0.98	1.00	1.40	-0.97	-0.10	1.63	-0.99	2.22	2.64	0.80	1.89	1.63	-0.76	0.25	1.40	-0.02	2.57	1.31	0.47	-0.11	0.07	1.70	2.79	2.91	0.67	-0.19	1.82	2.56	2.90	0.07	2.46	0.52	2.61	1.16	1.91	0.72	1.70	1.35	2.29	0.27	1.75	0.98	1.63	2.15	-0.03	1.86	1.40	-0.27	1.11	1.57	2.05	-0.17	1.95	2.51	-1.79	1.75	1.51	0.64	-0.97	0.81	3.07	-0.71	2.59	0.49	1.99	1.21	-0.61	1.68	-0.87	0.84	-1.36	-0.36	-2.88	-1.71	-0.25	0.20	-1.81	-0.26	-1.89	-2.45	-1.76	-1.13	-2.04	-0.77	-0.60	-0.54	-2.26	0.19	-0.13	-0.00	-1.60	1.32	-1.13	0.72	-1.22	-1.08	-1.02	-3.05	-1.27	2.15	-1.32	2.57	-0.46	-1.78	-0.84	-2.04	1.27	-2.24	-2.45	-1.47	0.51	-1.89	-1.03	0.87	1.06	-1.52	-1.50	-1.52	-2.49	-0.05	-1.16	0.42	-1.23	1.54	-1.40	-0.16	-3.10	0.46	-0.58	1.27	-1.83	1.17	-2.22	-0.92	1.55	-0.07	1.45	0.54	1.59	1.46	0.88	0.66	-0.17	1.25	1.34	0.84	2.09	0.27	-0.00	1.18	2.68	1.06	1.32	1.61	2.51	0.00	0.46	1.36	1.94	-1.24	1.59	1.61	1.44	1.08	1.62	-0.25	2.49	1.69	2.82	1.65	1.23	1.45	1.92	-0.33	2.71	2.93	1.93	4.42	1.96	-1.11	2.31	1.01	2.15	1.53	0.90	1.92	3.45	2.97	1.18	1.51	3.00	2.16	3.12	2.51	1.62	-1.51	2.05	3.04	2.51	1.89	2.14	1.60	2.21	2.36	0.81	2.61	2.55	2.34	2.81	2.16	3.28	2.12	4.18	2.63	2.90	2.89	0.94	0.24	2.70	1.85	2.20	2.01	2.30	0.35	2.38	1.98
2	-1.25	-2.54	-2.42	-1.95	-0.23	0.47	-2.27	1.83	1.78	0.59	1.42	-0.58	-2.72	-1.53	-1.21	-1.94	0.72	-0.77	1.10	-0.41	1.60	2.47	-1.59	-0.66	-1.19	-1.14	0.42	-0.02	0.81	-0.77	-0.34	-1.02	1.51	2.59	-1.96	2.41	-0.75	-1.07	2.14	-0.87	1.88	0.77	-0.15	0.20	-0.38	-0.31	1.39	-0.18	-0.31	-1.02	0.03	-1.04	1.73	2.00	-0.91	1.42	-0.68	1.24	-0.80	-0.68	-0.35	1.45	-1.09	-0.56	0.67	-1.16	-1.56	0.26	-0.57	1.48	1.57	1.28	1.52	0.70	-0.87	2.07	1.37	-0.79	0.50	-2.01	-1.58	-1.29	-2.08	0.11	-0.54	0.06	0.73	0.95	1.52	-0.31	1.35	1.06	0.99	-1.31	-0.04	2.37	1.31	1.70	1.80	1.32	1.28	-1.63	0.13	0.83	1.30	-1.22	1.27	1.57	1.42	2.69	2.35	1.82	1.87	2.27	1.06	1.44	1.41	1.28	1.89	1.25	1.56	2.09	0.88	1.36	2.53	1.18	2.53	2.97	1.80	2.57	2.24	2.10	1.46	1.68	1.55	2.42	-1.18	3.29	1.71	1.26	4.50	1.16	2.43	1.35	-1.30	2.72	-0.57	1.53	3.94	0.52	1.91	1.65	1.11	1.67	1.75	2.96	1.51	2.20	4.12	0.46	1.62	2.66	3.34	2.45	1.48	2.33	1.15	1.13	1.60	2.02	1.69	2.25	-1.91	2.61	1.99	-0.33	2.59	2.12	1.51	1.78	2.26	2.40	0.61	0.55	0.54	-0.30	1.74	1.93	2.71	1.37	1.98	2.82	-0.95	2.81	1.29	-1.19	-1.23	1.86	1.29	0.24	-0.46	0.44	1.06	0.44	-0.67	-2.54	0.78	1.29	1.08	1.18	0.95	1.21	0.98	1.33	-1.14	-1.40	1.03	1.00	0.26	0.75	1.61	1.90	1.77	-0.93	0.55	-0.17	-0.07	-0.09	1.61	1.19	-1.33	1.15	1.93	-0.86	-0.16	-1.05	0.40	1.46	-0.90	1.65	-0.41	1.16	2.01	1.76	0.75	0.21	0.95	1.57	0.60	1.20	-1.57	1.57	1.17	-0.98	0.83	1.51	0.68	0.97	1.01	1.38	-0.92	-0.21	1.66	-1.02	2.31	2.81	0.72	2.22	1.65	-0.63	0.39	1.64	-0.18	2.57	1.35	0.52	-0.49	-0.19	1.67	2.73	2.95	0.89	-0.07	1.82	2.34	2.94	0.06	2.17	0.47	2.17	1.16	1.91	0.82	1.50	1.10	2.21	-0.27	1.53	0.76	1.63	2.15	-0.31	1.80	1.43	-0.09	1.58	1.57	1.55	0.52	1.93	2.45	-1.75	1.67	1.56	0.85	-0.97	0.87	2.88	-0.64	2.46	0.49	2.15	1.38	-0.47	1.67	-0.74	0.86	-1.21	-0.25	-2.52	-1.79	-0.23	0.24	-1.84	-0.19	-1.73	-2.21	-1.69	-0.79	-2.04	-0.08	-0.50	-0.71	-2.28	-0.06	-0.03	-0.04	-1.53	1.59	-1.08	0.60	-1.04	-1.08	-1.22	-3.43	-1.18	2.15	-1.03	1.91	-0.56	-1.75	-0.91	-1.98	1.22	-2.17	-2.47	-1.47	0.59	-1.78	-1.13	0.92	1.04	-1.04	-1.27	-1.57	-2.40	0.03	-1.28	0.49	-1.16	1.23	-1.21	-0.24	-2.65	0.47	-0.55	1.27	-1.91	1.25	-2.25	-0.92	1.75	-0.07	1.31	0.43	1.53	1.09	0.88	0.58	-0.26	1.19	1.19	0.85	2.08	0.23	-0.29	0.91	2.61	0.98	1.29	1.51	2.84	-0.08	0.49	1.23	1.94	-1.44	1.57	0.81	1.44	0.61	1.64	-0.24	2.96	1.21	2.71	2.05	1.25	1.53	2.45	-0.63	2.72	2.68	1.97	4.42	2.55	-0.60	2.33	1.15	3.46	1.96	0.95	2.37	4.12	3.28	1.16	1.51	3.41	2.32	3.55	2.68	1.52	-1.54	2.29	3.02	2.71	1.66	2.09	1.57	2.18	2.34	0.92	2.79	2.32	2.34	2.91	2.22	3.10	2.10	4.37	2.65	2.76	3.00	0.85	0.27	2.48	1.98	2.25	1.84	2.35	0.30	2.46	2.27
3	-1.19	-2.28	-2.21	-1.92	-0.31	0.40	-2.71	1.81	1.69	0.50	1.58	-1.01	-2.44	-1.32	-1.18	-1.89	0.76	-0.97	1.20	-0.69	1.64	2.65	-1.85	-0.45	-1.12	-1.32	0.07	-0.23	0.79	-0.74	0.07	-1.05	1.51	2.79	-2.18	2.14	-0.59	-1.04	2.02	-0.66	1.78	0.77	-0.15	0.36	-0.35	-0.26	1.40	-0.65	-0.19	-1.05	0.15	-1.08	1.91	1.84	-1.22	1.24	-0.19	1.24	-0.81	-0.67	-0.33	1.21	-1.36	-0.53	0.57	-0.42	-1.60	0.55	-0.16	1.58	1.49	1.18	1.40	0.96	-1.31	1.81	1.31	-1.24	0.50	-2.01	-1.87	-1.62	-2.15	-0.05	-0.59	0.11	0.60	1.08	1.59	-0.70	1.34	0.74	0.78	-1.31	-0.28	1.47	1.14	1.73	1.55	1.15	1.27	-1.75	0.03	0.41	1.00	-1.23	1.02	1.53	1.24	2.56	2.21	1.69	1.61	2.03	0.84	1.38	1.37	1.12	1.82	1.19	1.39	1.77	0.61	1.22	2.38	1.02	2.42	2.94	1.94	2.40	1.85	2.12	1.52	1.60	1.55	2.18	-1.38	3.53	1.80	1.27	4.88	1.29	2.32	1.31	-1.19	2.88	-0.72	1.53	4.56	0.54	1.80	1.75	0.83	1.68	1.79	2.82	1.62	2.14	3.77	0.41	1.67	2.82	3.38	2.63	0.98	2.16	1.15	1.14	1.60	2.01	1.63	2.37	-1.91	2.62	2.10	-0.55	2.56	2.12	1.68	1.87	2.46	2.48	0.70	0.88	0.90	-0.67	1.74	2.13	2.63	1.25	2.08	3.01	-0.81	2.40	1.26	-1.19	-1.24	1.42	1.39	-0.46	-0.46	0.12	0.77	0.39	-0.69	-2.62	0.91	1.21	0.75	1.18	0.84	1.26	0.89	1.33	-1.27	-1.46	1.04	0.50	0.38	0.63	1.42	1.80	1.49	-1.08	0.55	-0.41	0.11	0.12	1.54	1.19	-1.40	1.21	1.61	-1.08	-0.35	-1.05	0.31	1.57	-0.90	1.37	-0.41	1.32	1.77	1.81	0.75	0.14	0.97	1.34	0.59	1.01	-1.33	0.28	1.17	-1.01	0.74	1.27	0.68	0.97	0.75	1.06	-0.91	-0.21	1.51	-1.04	2.22	2.94	0.72	2.33	1.66	-0.50	0.58	1.46	-0.05	2.39	1.24	0.36	-0.46	-0.22	1.78	2.73	2.50	0.78	0.18	1.82	1.94	2.85	0.06	2.26	0.97	2.15	1.16	1.91	0.98	1.50	0.88	1.77	-0.70	1.64	0.86	1.68	2.03	-0.14	1.84	1.47	-0.15	1.96	1.57	1.42	0.65	1.90	2.26	-1.71	1.67	1.46	0.59	-1.02	0.90	2.88	-0.47	2.49	0.78	2.15	0.89	-0.47	1.67	-0.46	0.88	-1.12	-0.24	-2.56	-2.46	-0.22	0.20	-1.76	-0.12	-1.73	-2.23	-1.71	-0.99	-2.22	-0.49	-0.64	-0.52	-2.22	-0.13	-0.14	-0.08	-1.53	1.63	-0.89	0.60	-1.01	-1.09	-1.20	-2.96	-1.24	1.96	-0.60	1.47	-0.56	-2.03	-1.01	-1.89	1.16	-2.27	-2.25	-1.40	0.64	-1.88	-1.07	0.91	0.99	-0.97	-1.27	-1.33	-2.40	0.07	-1.36	0.49	-1.19	1.26	-1.31	-0.25	-2.72	0.45	-0.63	1.86	-1.79	1.25	-2.11	-0.92	1.72	-1.28	1.32	0.41	1.43	0.91	0.84	0.60	-0.35	1.04	1.11	0.69	2.11	0.00	0.01	0.87	2.59	1.04	1.24	1.43	2.36	-0.09	0.26	1.21	1.58	-1.17	1.59	0.71	1.50	0.61	1.44	-0.01	2.96	1.54	2.44	2.23	1.25	1.60	2.74	-0.16	2.80	3.01	2.28	4.15	1.94	-0.78	2.31	1.31	3.05	1.92	0.96	1.97	3.83	2.98	0.99	1.46	3.43	2.32	3.48	2.78	1.51	-1.58	2.17	2.60	2.53	1.82	2.16	1.40	2.28	2.43	0.88	2.86	2.42	2.25	2.70	2.41	2.96	2.00	4.20	2.57	2.72	2.98	0.75	0.24	2.40	1.96	2.20	1.91	2.19	0.23	2.50	2.25
4	-1.23	-2.22	-2.20	-2.10	-0.41	0.32	-2.75	1.75	1.47	0.45	1.58	-0.82	-2.37	-1.13	-1.21	-1.99	0.72	-1.22	1.03	-0.72	1.58	2.59	-2.12	-0.95	-1.19	-1.43	-0.06	-0.43	0.79	-0.72	-0.09	-0.91	1.39	2.63	-2.13	2.29	-0.82	-1.08	1.84	-0.75	1.64	0.60	-0.12	0.34	-0.96	-0.83	1.40	-0.70	-0.37	-1.12	0.24	-0.96	1.55	1.84	-1.19	1.27	-0.47	1.24	-1.30	-0.50	-0.53	1.12	-1.42	-0.56	0.69	-0.87	-1.64	0.05	-0.70	1.51	1.51	1.10	1.40	0.58	-1.19	1.63	1.31	-1.17	0.15	-1.79	-1.87	-1.58	-2.18	-0.14	-0.54	-0.16	0.26	1.08	1.50	-0.74	1.40	0.79	0.61	-1.58	-0.60	1.23	1.12	1.60	1.38	1.14	1.23	-1.74	-0.11	0.41	1.12	-1.15	1.04	1.53	1.10	2.42	2.14	1.61	1.51	1.92	0.71	1.51	1.26	1.03	1.66	0.89	1.32	1.79	0.56	1.22	2.20	0.89	2.30	2.92	1.94	2.48	1.87	2.12	1.52	1.60	1.55	2.08	-1.38	3.14	1.75	1.03	4.55	1.20	2.45	1.35	-1.26	2.54	-0.85	1.53	4.18	0.62	1.80	1.70	0.68	1.82	1.78	2.77	1.55	1.99	3.49	0.26	1.65	2.60	3.12	2.52	0.98	2.16	1.15	1.07	1.64	2.00	1.56	2.20	-2.40	2.45	1.68	-0.57	2.21	2.12	1.45	1.87	2.46	2.17	0.80	0.72	0.87	-0.26	1.74	1.88	2.39	1.34	1.78	2.69	-0.92	2.53	1.28	-1.13	-1.24	1.64	1.33	-0.10	-0.46	0.36	0.52	0.48	-0.67	-2.34	1.01	1.22	0.75	1.02	0.75	1.13	0.90	1.49	-1.30	-0.99	0.83	0.50	0.50	0.63	1.42	1.85	1.49	-1.29	0.41	-0.29	0.08	-0.32	1.54	1.10	-1.37	1.30	1.56	-1.20	-0.74	-1.05	0.51	1.27	-0.90	1.37	-0.41	1.19	1.73	1.67	0.75	0.04	0.91	1.35	0.59	0.95	-0.86	0.28	0.89	-1.23	0.74	1.27	0.67	1.10	0.75	1.13	-0.92	-0.20	1.48	-1.02	2.25	2.81	0.67	1.80	1.69	-0.50	0.52	1.37	-0.13	2.40	1.27	0.60	-0.19	-0.22	1.65	2.79	1.89	0.85	0.20	1.82	1.85	2.45	0.19	2.26	0.56	1.74	1.26	1.91	0.87	1.51	0.60	1.88	-0.74	1.67	0.68	1.68	1.96	0.09	1.77	1.11	-0.15	1.96	1.57	1.28	0.89	1.72	2.24	-1.72	1.55	1.47	0.73	-1.02	0.97	2.85	-0.49	2.51	0.78	1.76	1.11	-0.47	1.52	-0.69	0.78	-1.14	-0.13	-2.28	-1.61	-0.31	0.20	-1.67	-0.00	-1.63	-2.21	-1.73	-0.92	-2.09	-0.56	-0.81	-0.54	-2.51	-0.54	-0.28	-0.08	-1.53	1.10	-0.60	0.60	-0.99	-1.15	-1.22	-2.75	-1.28	2.02	-0.63	1.47	-0.51	-2.03	-0.88	-1.87	1.21	-2.11	-2.20	-1.32	0.64	-1.86	-1.01	1.03	1.06	-1.31	-1.32	-1.23	-2.88	0.04	-0.93	0.49	-1.24	1.43	-1.29	-0.14	-2.87	0.44	-0.46	1.86	-1.65	1.20	-1.98	-0.94	1.77	-1.28	1.26	0.42	1.28	1.27	0.85	0.55	-0.48	1.11	1.08	0.60	2.04	-0.01	-0.13	0.87	2.40	0.82	1.44	1.30	2.36	0.09	0.33	1.30	1.58	-1.19	1.59	0.15	1.50	0.95	1.44	-0.83	2.68	1.32	2.44	1.98	1.30	1.25	2.27	-0.02	2.80	3.01	2.01	3.88	1.94	-1.06	2.21	1.14	2.45	1.86	0.73	1.97	3.48	2.57	0.99	1.46	3.43	2.32	3.26	2.63	1.39	-1.43	1.99	2.60	2.38	1.82	1.92	1.32	2.19	2.37	0.78	2.59	2.32	2.33	2.63	2.36	2.93	1.96	4.03	2.47	2.78	2.54	0.74	0.43	2.40	1.85	2.06	1.75	2.08	0.29	2.43	2.30

模拟实验３¶

降维分析¶

主成分分析 ¶

因子分析 ¶

独立成分分析 ¶

多维尺度分析 ¶

t-SNE ¶

比较各种方法下特征与y的xicor相关系数¶